Bob wants to find the area of an irregular shape. He cuts a piece of string to the length of the perimeter of the shape.

He measures to see that the string is about 60 cm long. Bob then forms his string into a square on top of centimeter graph paper.

Using the graph paper, he determines that the area of his string square is about 225 cm2.

Bob says that the area of the irregular shape is therefore also 225 cm2.

Is Bob’s method for determining the area of the irregular shape valid or not? Explain. If the method is not valid, what can you determine about the area of the irregular shape from the information that Bob has? Explain.

Bob's method for determining the area of the irregular shape is not valid. While it's true that he can form a square with the same perimeter as the irregular shape, it doesn't necessarily mean that the area of the square is equal to the area of the irregular shape.

In this case, Bob's string forms a square with an area of 225 cm², but the irregular shape may have a different area. The irregular shape could have a smaller or larger area compared to the square, depending on its specific dimensions and configuration.

What Bob can determine from his method is that the irregular shape has a perimeter equal to the perimeter of the square formed by the string (60 cm). However, without further information or a different approach, he cannot accurately determine the exact area of the irregular shape.

To find the area of the irregular shape, Bob would need to use a different method such as breaking it down into smaller, regular shapes whose areas can be calculated or using formulas specific to the shape's geometry. Alternatively, he could use more advanced mathematical techniques such as integration if the irregular shape's boundaries are known.